Options[saveData] = {Method -> "Addition"};
saveData[vars_, opts : OptionsPattern[{saveData}]] :=
  saveData[vars, OptionValue[Method]]
saveData[vars_, "Addition"] := Total @ vars
saveData[vars_, "Multiplication"] := Times @@ vars

saveData[{1, 2, 3}, Method->"Multiplication"]
(* 6 *)
saveData[{a, b, c}, Method->"Addition"]
(* a + b + c *)

<method-opt> = ( 'Method' , <rule-arrow> ) | ( <opt-spec> | <core-method> ) ;
 <opt-head> = 'Method' | 'WorkingPrecision' | 'Delimiter' ;
 <core-method> = 'Addition' | 'Multiplication' | 'CompensatedSummation' ;
 <opt-rule> = <opt-head> , <rule-arrow> | ( <core-method> | <opt-value> | <opt-spec> ) ;
 <opt-value> = '_String' ;
 <opt-spec> = '{' | <core-method> , [ ',' | <opt-list> ] | '}' ;
 <opt-list> = <opt-rule> , { ',' | <opt-rule> } ;
 <rule-arrow> = '->' | '[Rule]' ;

"Method -> {Multiplication, Method -> {CompensatedSummation, WorkingPrecision -> 40}}"

"Method -> {Addition, Method -> CompensatedSummation, WorkingPrecision -> 34}"

<method-opt> = ( 'Method' , <rule-arrow> ) |> <opt-spec> ;
 <opt-spec> = <add-method> | <mult-method> ;
 <opt-head> = 'Method' | 'WorkingPrecision' | 'Delimiter' ;
 <add-method> = 'Addition' | '{' | 'Addition' , [ ',' | <add-opt-list> ] | '}' ;
 <mult-method> = 'Multiplication' | '{' | 'Multiplication' , [ ',' | <mult-opt-list> ] | '}' ;
 <compsum-method> = 'CompensatedSummation' | '{' | 'CompensatedSummation' , [ ',' | <compsum-opt-list> ] | '}' ;
 <add-opt-list> = <add-opt-rule> , { ',' | <add-opt-rule> } ;
 <mult-opt-list> = <mult-opt-rule> , { ',' | <mult-opt-rule> } ;
 <compsum-opt-list> = <compsum-opt-rule> , { ',' | <compsum-opt-rule> } ;
 <add-opt-rule> = ( 'Method' | 'Delimiter' ) , <rule-arrow> | ( <opt-value> |  <compsum-method> ) ;
 <mult-opt-rule> = 'Delimiter', <rule-arrow> |> <opt-value> ;
 <compsum-opt-rule> = 'WorkingPrecision', <rule-arrow> | <opt-value> ;
 <opt-value> = '_String' ;
 <rule-arrow> = '->' | '[Rule]' ;

Options[saveData] = {Method -> Automatic};
$MethodValues = {"Addition", "Multiplication", Automatic};

saveData::bdmtd =
   "Value of Method -> `` is not one of " <> ToString@$MethodValues;

saveData[vars_, opts : OptionsPattern[]] :=
  Module[{mtd},
   mtd = OptionValue[Method];
   If[! MemberQ[$MethodValues, mtd],
    Message[saveData::bdmtd, mtd];
    Return[$Failed]
   ];
   Switch[mtd,
    Automatic | "Addition",
    Total@vars,
    "Multiplication",
    Times @@ vars
   ]
 ]

saveData[{1, 2, 3}, Method -> "1"]
saveData[{1, 2, 3}, Method -> "Multiplication"]
saveData[{a, b, c}, Method -> "Addition"]